SSC Selection Post 2023 PYQ — Question 63

The correct answer is Option 2 i.e. 3.5 cm.

Volume of hemisphere(V) = $2\over3$πR³

here, R = radius of hemisphere

Volume of hemisphere = $2\over3$ × 7³ × π = $686\over3$π

Let the radius of each small sphere = r

Volume of 4 small spheres = 4 × $4\over3$πr³ = $16\over3$πr³

According to the question,

⇒ $686\over3$π = $16\over3$πr³

⇒ r³ = 42.875

⇒​​​​​​​ r = 3.5 cm